局部波动率的深度自洽学习
Deep self-consistent learning of local volatility
AI总结：
本文提出用深度神经网络同时逼近市场期权价格和局部波动率，通过自洽求解 Dupire 方程并施加无套利软约束，在合成与市场数据上验证了该方法能降低插值和重定价误差并提升波动率平滑性。
摘要：
我们提出了一种通过深度自洽学习从市场期权价格校准局部波动率的算法，该算法使用深度神经网络同时逼近市场期权价格和局部波动率。我们的方法利用由参数化期权价格求解的底层 Dupire 偏微分方程的初边值问题，以自洽的方式对参数化进行修正。通过利用神经网络的可微性，我们可以在每个行权价-到期日对上局部地评估 Dupire 方程；同时，通过利用神经网络的连续性，我们从给定域中均匀采样行权价-到期日对，超越了期权报价所在的离散点。此外，通过惩罚相关的损失函数作为软约束来施加无套利机会条件。为了与现有方法进行比较，所提出的方法在合成期权价格和市场期权价格上均进行了测试，结果表明在降低插值误差和重新定价误差以及校准局部波动率的平滑性方面具有改进的性能。我们还进行了消融研究，证实了所提出方法的鲁棒性和重要性。
英文摘要：
We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the initial-boundary value problem of the underlying Dupire's partial differential equation solved by the parameterized option prices to bring corrections to the parameterization in a self-consistent way. By exploiting the differentiability of neural networks, we can evaluate Dupire's equation locally at each strike-maturity pair; while by exploiting their continuity, we sample strike-maturity pairs uniformly from a given domain, going beyond the discrete points where the options are quoted. Moreover, the absence of arbitrage opportunities are imposed by penalizing an associated loss function as a soft constraint. For comparison with existing approaches, the proposed method is tested on both synthetic and market option prices, which shows an improved performance in terms of reduced interpolation and reprice errors, as well as the smoothness of the calibrated local volatility. An ablation study has been performed, asserting the robustness and significance of the proposed method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
